A noted psychic was tested for ESP. The psychic was presented with 200 cards face down and was asked to determine if the card was one of 5 symbols: a star, cross, circle, square, or three wavy lines. The psychic was correct in 49 cases. Let $p$ represent the probability that the psychic correctly identifies the symbol on the card in a random trial. Assume the 200 trials can be treated as an SRS from the population of all guesses.
To see if there is evidence that the psychic is doing better than just guessing, we test

(a) What is the $z$-statistic for this test?

(b) What is the P-value of the test?